| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Easy -1.2 This is a straightforward application of standard arithmetic sequence formulas (nth term and sum) with clear given values. Part (a) and (b) require direct substitution into formulas, while part (c) involves solving a simple quadratic equation. The real-world context adds no mathematical complexity, and all three parts are routine textbook exercises requiring only recall and basic algebraic manipulation. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(T_{20} = 140 + (20-1)(20) = 520\) | M1 | Attempt to use formula for 20th term of AP with \(a=140\), \(d=20\) |
| \(= 520\) | A1 | For 520 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(S_{20} = \frac{20}{2}(2\times140+(20-1)(20))\) or \(\frac{20}{2}(140+520)\) | M1 | Attempt to apply \(\frac{1}{2}n(2a+(n-1)d)\) or \(\frac{1}{2}n(a+l)\) with their values |
| Uses \(a=140\), \(d=20\), \(n=20\); ft on their \(l\) from (a) | A1 | Uses correct values |
| \(= 6600\) | A1 | 6600 cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(8500 = \frac{n}{2}(300+700)\) | M1 | Attempt to use \(S_n = \frac{n}{2}(a+l)\) with \(a=300\), \(l=700\), \(S=8500\) |
| Correct equation set up | A1 | Uses formula with correct values |
| \(\Rightarrow n = 17\) | A1 | Finds exact value 17 |
## Question 7:
### Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $T_{20} = 140 + (20-1)(20) = 520$ | M1 | Attempt to use formula for 20th term of AP with $a=140$, $d=20$ |
| $= 520$ | A1 | For 520 |
### Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $S_{20} = \frac{20}{2}(2\times140+(20-1)(20))$ or $\frac{20}{2}(140+520)$ | M1 | Attempt to apply $\frac{1}{2}n(2a+(n-1)d)$ or $\frac{1}{2}n(a+l)$ with their values |
| Uses $a=140$, $d=20$, $n=20$; ft on their $l$ from (a) | A1 | Uses correct values |
| $= 6600$ | A1 | 6600 cao |
### Part (c)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $8500 = \frac{n}{2}(300+700)$ | M1 | Attempt to use $S_n = \frac{n}{2}(a+l)$ with $a=300$, $l=700$, $S=8500$ |
| Correct equation set up | A1 | Uses formula with correct values |
| $\Rightarrow n = 17$ | A1 | Finds exact value 17 |\begin{enumerate}
\item Lewis played a game of space invaders. He scored points for each spaceship that he captured.
\end{enumerate}
Lewis scored 140 points for capturing his first spaceship.\\
He scored 160 points for capturing his second spaceship, 180 points for capturing his third spaceship, and so on.
The number of points scored for capturing each successive spaceship formed an arithmetic sequence.\\
(a) Find the number of points that Lewis scored for capturing his 20th spaceship.\\
(b) Find the total number of points Lewis scored for capturing his first 20 spaceships.
Sian played an adventure game. She scored points for each dragon that she captured. The number of points that Sian scored for capturing each successive dragon formed an arithmetic sequence.
Sian captured $n$ dragons and the total number of points that she scored for capturing all $n$ dragons was 8500 .
Given that Sian scored 300 points for capturing her first dragon and then 700 points for capturing her $n$th dragon,\\
(c) find the value of $n$.\\
\hfill \mbox{\textit{Edexcel C1 2013 Q7 [8]}}